The number of revolutions per second made by an electron in the first Bohr orbit of a hydrogen atom is of the order of

$A$ small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2} m \omega^2 r^2$,where $\omega$ is a constant and $r$ is the distance of the particle from the origin. Assuming Bohr's quantization of angular momentum and a circular orbit,the radius of the $n^{\text{th}}$ orbit will be proportional to:

The radius of the orbit of an electron in a Hydrogen-like atom is $4.5 a_0$,where $a_0$ is the Bohr radius. Its orbital angular momentum is $\frac{3h}{2\pi}$. It is given that $h$ is Planck constant and $R$ is Rydberg constant. The possible wavelength$(s)$,when the atom de-excites,is (are) :
$(A)$ $\frac{9}{32R}$ $(B)$ $\frac{9}{16R}$ $(C)$ $\frac{9}{5R}$ $(D)$ $\frac{4}{3R}$

Suppose an electron is attracted towards the origin by a force $F = \frac{k}{r}$,where $k$ is a constant and $r$ is the distance of the electron from the origin. By applying the Bohr model to this system,the radius of the $n^{th}$ orbital of the electron is found to be $r_n$ and the kinetic energy of the electron is $K_n$. Then which of the following is true?

The de Broglie wavelength of an electron in the first orbit of Bohr's model is . . . . . . .

The de-Broglie wavelength of an electron in the first Bohr orbit is